What does this icon mean - circle next to a child in blender
That is the icon of a Material datablock, it means there is a material assigned directly to the mesh data, as opposed to the object itself.

When creating or editing Material Slots you have two options when assigning a material, it can be either assigned to the Object or the Object Data.

When assigned to the object, several object clones or instances of that object (while sharing the same geometry or mesh data) can have different materials regardless, but if the material is assigned to the Object Data all instances will forcefully have that same material.

Each materials assigned to Object Data will display one additional icon to the side of the data it is bound to in the Outliner, other materials show up below.